Global climate modeling of Saturn's atmosphere. Part III: Global statistical picture of zonostrophic turbulence in high-resolution 3D-turbulent simulations

Abstract

We conduct an in-depth analysis of statistical flow properties calculated from the reference high-resolution Saturn simulation obtained by global climate modelling in Part II. In the steady state of this reference simulation, strongly energetic, zonally dominated, large-scale structures emerge, which scale with the Rhines scale. Spectral analysis reveals a strong anisotropy in the kinetic energy spectra, consistent with the zonostrophic turbulent flow regime. By computing spectral energy and enstrophy fluxes we confirm the existence of a double cascade scenario related to 2D-turbulent theory. To diagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere, we run a set of four simulations using an idealized version of our Global Climate Model devoid of radiative transfer, with a well-defined Taylor-Green forcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn's rotation rate). This allows us to identify dynamics in three distinctive inertial ranges: (1) a "residual-dominated" range, in which non-axisymmetric structures dominate with a −5/3 spectral slope; (2) a "zonostrophic inertial" range, dominated by axisymmetric jets and characterized by the pile-up of strong zonal modes with a steeper, nearly −3, spectral slope; and (3) a "large-scale" range, beyond Rhines' typical length scale, in which the reference Saturn simulation and our idealized simulations differ. In the latter range, the dynamics is dom- * Corresponding author. inated by long-lived zonal modes 2 and 3 when a Saturn-like seasonal forcing is considered (reference simulation), and a steep energetic decrease with the idealized Taylor-Green forcing. Finally, instantaneous spectral fluxes show the coexistence of upscale and downscale enstrophy/energy transfers at large scales, specific to the regime of zonostrophic turbulence in a 3D atmosphere.

Global climate modeling of Saturn’s atmosphere. Part IV: Stratospheric equatorial oscillation

“…Using this GCM tailored for Saturn, Spiga et al (2020) simulated Saturn's atmosphere from the troposphere to the lower stratosphere for 15 Saturn years at fine horizontal resolution, without any prescribed sub-grid-scale wave parameterization. The DYNAMICO-Saturn GCM simulation described in Spiga et al (2020) produced consistent thermal structure and seasonal variability compared to Cassini CIRS measurements, mid-latitude eddy-driven tropospheric eastward and westward jets commensurate to those observed (and following the zonostrophic regime -see Section 3 for details -as is argued in the part III paper by Cabanes et al (2020)), and planetary-scale waves such as Rossby-gravity (Yanai), Rossby and Kelvin waves in the tropical waveguide. While the simulations in Spiga et al (2020) exhibited stacked eastward and westward jets in the equatorial stratosphere, those jets were not propagating downwards, contrary to the observed equatorial oscillation.…”

“…What Figs. 3 and 4 also show is that the eddy spectra is different in our 61-level simulation compared to the 32-level simulation analyzed in Spiga et al (2020) and Cabanes et al (2020). In the 32-level simulation, the tropospheric residual spectrum barely fits the wellknown Kolmogorov-Kraichnan (KK) law 2∕3 −5∕3 (Kraichnan, 1967a) evocative of the inverse turbulent cascade with the energy transfer rate = 2 × 10 −6 W kg −1 .…”

“…In all simulations, spectral fluxes clearly show the predominance of an inverse cascade of energy at large scale and a direct cascade of enstrophy at small scale. This energy-enstrophy double cascade scenario is a well-known feature of quasi-two-dimensional (2D) turbulence, when a turbulent flow is made quasi-2D by confinement to a shallow atmosphere and under rapid planetary rotation (Pouquet and Marino, 2013;Cabanes et al, 2020). For the 32-level simulation, Cabanes et al (2020) showed that the inverse cascade of energy results from the barotropization of baroclinic eddies at small scales and drives the large scale atmospheric flow.…”

“…This dynamical regime is referred to as zonostrophic macroturbulence (Sukoriansky et al, 2002;Galperin et al, 2014). Further discussions on this topic can be found in the Part III paper Cabanes et al (2020).…”

“…We now extend our comparison by computing the spherical harmonic decomposition of horizontal velocity maps from our 61-level simulation, using the same tools as in the Part III paper (Cabanes et al, 2020) for the 32-level simulation. When spherical harmonic functions are invoked, energy spectra depend on non-dimensional total and zonal indices and respectively (Boer, 1983).…”